The rubens' tube works because, as the soundwaves move through the pipe, the changes in pressure make the the flames spring up or die down as the music plays. Ultimately, the pyro board (like the ruben's tube) works on the same basic principles: It produces a distinct pattern of flames on top that constantly change based on what's being played.
If you want to know the specifics, this works because the flow is proportional to the square root of the pressure difference between the gas inside the hole and the air outside. When the sound that is being pumped through the pipe goes up, the pressure gets so high at the antinodes that all the gas is pushed out of the tube, making the jet of fire spurt really high as flaming gas exits the tube. Then is obviously dips to normal as the next soundwave comes along and gives it the proper elevation.
And a final video, piano style.